On the logarithmic Petrovsky equation with distributed delay: existence, decay, and blow up

In this article, we deal with a logarithmic Petrovsky equation with distributed internal delay. Firstly, we prove the local existence of solutions utilizing the semigroup theory. Later, we obtain the global existence of solutions by using the well-depth method. Moreover, under appropriate assumptions on the weight of the delay and that of frictional damping, we get the exponential decay. Finally, we establish the blow up of solutions.